∫ (((x2+2)a(x +tan-1x)/x2+1))dx =

Question

∫ (((x2+2)a(x +tan-1x)/x2+1))dx =  (A) log a.ax+tan-1x+c (B) ((x+tan-1x)/log a)+c (C) (ax+tan-1x/log a)+c (D) log a(x + tan-1x) + c

Tardigrade Admin · Accepted Answer

Let I=∫ ((x2+2) a(x+ tan -1 x)/x2+1) dx Put x+ tan -1 x=t ⇒ (1+(1/1+x2)) dx=dt ⇒ (2+x2/1+x2) dx=dt ∴ I =∫ at dt=(at/ log a)+c =(ax+ tan -1 x/ log a)+c

Q. $\int (\frac{( x ^{2} + 2 ) a ^{(x + t a n^{- 1} x)}}{x ^{2} + 1}) d x =$

$l o g a . a^{x + t a n^{- 1} x} + c$

$\frac{( x + t a n ^{- 1} x )}{l o g a} + c$

$\frac{a ^{x + t a n^{- 1} x}}{l o g a} + c$

$l o g a (x + t a n^{- 1} x) + c$

Q. ∫(x2+1(x2+2)a(x+tan−1x)​)dx=

loga.ax+tan−1x+c

loga(x+tan−1x)​+c

logaax+tan−1x​+c

loga(x+tan−1x)+c

Let I=∫x2+1(x2+2)a(x+tan−1x)​dx Put x+tan−1x=t ⇒(1+1+x21​)dx=dt ⇒1+x22+x2​dx=dt ∴I=∫atdt=logaat​+c =logaax+tan−1x​+c

Q. $\int (\frac{( x ^{2} + 2 ) a ^{(x + t a n^{- 1} x)}}{x ^{2} + 1}) d x =$

$l o g a . a^{x + t a n^{- 1} x} + c$

$\frac{( x + t a n ^{- 1} x )}{l o g a} + c$

$\frac{a ^{x + t a n^{- 1} x}}{l o g a} + c$

$l o g a (x + t a n^{- 1} x) + c$